On saddle submanifolds of Riemannian manifolds

Saddle submanifolds are considered. A characterization of such submanifolds of Euclidean space is given in terms of sectional curvature. Extending results of T. Frankel, K. Kenmotsu and C. Xia, we determine under what conditions two complete saddle submanifolds of a complete connected Riemannian manifold (M) over bar, with nonnegative k-Ricci curvature, must intersect. Moreover, if (M) over bar has positive k-Ricci curvature and the dimension of a compact saddle submanifold satisfies a certain inequality then we show that the homomorphism of the fundamental groups pi(1)(M) and pi(1)((M) over bar) is surjective.